A nanocomposite based on a styrene-acrylate copolymer and native montmorillonite clay 1. Preparation, testing, and properties

The preparation of a polymer nanocomposite by compounding an aqueous polymer emulsion with an aqueous dispersion of montmorillonite clay is described. A styrene-acrylate copolymer emulsion and a purified native montmorillonite clay from Latvian deposits are used. An X-ray diffraction analysis and differential scanning calorimetric thermograms are shown. Data on the influence of montmorillonite concentration on the tensile stress-strain diagram, elasticity, yield stress, breaking stress, and ultimate elongation of the processed nanocomposite material are obtained. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 61–74, January–February, 2006.     

Moisture permeability of a polymer nanocomposite containing unmodified clay

Results of an investigation into the kinetics of moisture sorption by an unfilled styrene-acrylate copolymer and a nanocomposite containing unmodified montmorillonite clay are reported. The sorption tests were performed at 25°C and different levels of the relative humidity of air up to 80%. The moisture diffusivity was calculated using Fick's equation for one-dimensional diffusion. Data on the influence of montmorillonite concentration on the coefficients of diffusion, solubility, and permeability are obtained. The experimental values of the permeability coefficient are compared with those calculated by using a model taking into account the increased path of a diffusing water molecule caused by the shielding effect of plate like filler particles. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 723–736, September–October, 2008.     

Nanocomposites based on a styrene-acrylate copolymer and organically modified montmorillonite 1. Mechanical properties

The preparation of polymer nanocomposites by mixing a solution of a styrene-acrylate copolymer with a suspension of organically modified montmorillonite in dimethyl formamide is described. Seven different compositions with organomontmorillonite content from 0 to 7 wt.% were prepared and tested. Results of their X-ray diffraction analysis are presented. Data on the influence of organomontmorillonite content on the tensile stress-strain curves, elastic modulus, strength, and ultimate elongation of the nanocomposites are obtained. The concentration dependences of elastic properties of materials with differently oriented platelike nanoparticles is analyzed by using an algorithm elaborated for stepwise calculations of elastic constants with account of the features of structural hierarchy of intercalated and exfoliated nanocomposites. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 375–388, May–June, 2006.     

A nanocomposite based on a styrene-acrylate copolymer and organically modified montmorillonite 2. Barrier and thermal properties

The results of an investigation into the barrier and thermal properties of polymer nanocomposites prepared by blending a styrene-acrylate copolymer solution with a suspension of organically modified montmorillonite are presented. The influence of organomontmorillonite content on the barrier properties of the nanocomposite is investigated with the example of water vapor permeability. The experimental values of the permeability coefficient are compared with those calculated by using a model taking into account the increased path of diffusing water molecules caused by the shielding effect of plate like particles. The thermograms of differential scanning calorimetry in the temperature range from −40 to 130°C are presented. The results of a thermogravimetric analysis for specimens heated in air to 800°C are also reported. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 503–516, July–August, 2006.     

A nanocomposite based on a styrene-acrylate copolymer and native montmorillonite clay 2. Modeling the elastic properties

A variant of stepwise determination of the elastic characteristics of quasi-isotropic polymer-silicate nanocomposites with randomly oriented platelike filler particles is considered. First, the elastic constants of transversely isotropic structural elements with coplanarly placed filler particles are obtained, and then they are averaged over all spatial directions by using the orientational averaging method. The characteristic features of the hierarchical structure of exfoliated and intercalated nanocomposites are also considered. The concentration dependences of elastic constants of a nanocomposite based on a styrene-acrylate copolymer and native montmorillonite clay are modeled, and the results obtained are compared with experimental data. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 235–246, March–April, 2006.     

Effect of anisometry of a platelike nanofiller on the elastic constants of a transversely isotropic composite

Analysis results for the elastic properties of a composite with a small amount of coplanarly arranged platelike filler particles are presented. The geometrical form of the particles is described by an oblate ellipsoid of revolution. The calculations are performed by formulas obtained by using the Eshelby approach for media with a low concentration of inclusions. The effect of anisometry of the ellipsoidal particles and of the ratio between the elastic moduli of the filler and matrix on the effective elastic constants of the composite is discussed. Calculation results are compared with experimental data for the elastic moduli of a nanocomposite containing completely exfoliated particles of an unmodified montmorillonite. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 493–504, July–August, 2008.     

Elasticity of composites with irregularly oriented shape-anisotropic filler particles

A variant of determining the elastic characteristics of composites containing irregularly oriented shape-anisotropic filler particles of two types (short fibers and thin platelets) is considered. The effective elastic constants of the composites are calculated by using the method of orientational averaging of elastic characteristics of isolated transversely isotropic structural elements reinforced with unidirectionally oriented short fibers or coplanarly arranged thin platelets. The superposition of elastic properties of the irregularly oriented structural elements, with account of their orientational distribution in the composite material, is accepted. The calculation results are compared with experimental data for the effective elastic moduli of polymeric composites reinforced with short glass fibers and of polymeric nanocomposites containing the platelet-type particles of organically modified montmorillonite. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 285–300, May–June, 2006.     

A unified local convergence analysis of inexact constrained Levenberg–Marquardt methods

The Levenberg–Marquardt method is a regularized Gauss–Newton method for solving systems of nonlinear equations. If an error bound condition holds it is known that local quadratic convergence to a non-isolated solution can be achieved. This result was extended to constrained Levenberg–Marquardt methods for solving systems of equations subject to convex constraints. This paper presents a local convergence analysis for an inexact version of a constrained Levenberg–Marquardt method. It is shown that the best results known for the unconstrained case also hold for the constrained Levenberg–Marquardt method. Moreover, the influence of the regularization parameter on the level of inexactness and the convergence rate is described. The paper improves and unifies several existing results on the local convergence of Levenberg–Marquardt methods.     

Buckling of stepped composite columns

The stability of elastic columns subjected to axial pressure is studied. An elastic multistepped column with rectangular cross sections are considered assuming that at the re-entrant corners of the column stable cracks are located. The influence of a crack on the loss of stability of the column is described by means of local flexibility and the function of compliance coupled with the stress intensity factor, which is known from the linear elastic fracture mechanics. A column with a single step is studied in more detail. The influence of crack location and length on the buckling load is assessed numerically. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 87–100, January–February, 2006.     

A refined stress-strain analysis in the load transfer zone of flat specimens of high-strength unidirectional composites in uniaxial tension 3. Effect of grip misalignment

The influence of a preliminary bending induced by misalignment of the grips of a testing machine on the stress-strain state of a flat specimen made of a high-strength unidirectional carbon fiber composite under uniaxial tension is estimated. An analysis of the analytical solution obtained is carried out, and the results of finite-element calculations and modeling experiments are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 745–760, November–December, 2007.     

On the propagation of Lamb waves in a sandwich plate made of compressible materials with finite initial strains

The propagation of flexural Lamb waves in a prestrained sandwich plate made from compressible highly elastic materials is investigated within the scope of a piecewise homogeneous body model by utilizing TLTEWISB. The mechanical relations of layer materials are described by a harmonic-type potential, and numerical results are obtained for the first and second vibration modes. According to the results, the influence of problem parameters and of the initial stretching strain along the layers on the wave propagation speed is examined. The asymptotic values of the speed are considered in the cases of short and long wavelengths, and the influence of the initial strains on these asymptotic (limit) values are also analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 231–244, March–April, 2008.     

Variation of the structure and permeability of tensioned fiber layers during impregnation with a thermoplastic polymer melt

The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation. Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000.     

Automorphisms of Maps with a Given Underlying Graph and Their Application to Enumeration

A graph is called a semi-regular graph if its automorphism group action on its ordered pair of adjacent vertices is semi-regular. In this paper, a necessary and sufficient condition for an automorphism of the graph F to be an automorphism of a map with the underlying graph F is obtained. Using this result, all orientation-preserving automorphisms of maps on surfaces (orientable and non-orientable) or just orientable surfaces with a given underlying semi-regular graph F are determined. Formulas for the numbers of non-equivalent embeddings of this kind of graphs on surfaces (orientable, non-orientable or both) are established, and especially, the non-equivalent embeddings of circulant graphs of a prime order on orientable, non-orientable and general surfaces are enumerated.     

Heat transfer in sliding of a plane-parallel layer over a base

An analytic solution of the thermal problem of friction for a plane-parallel layer–base tribosystem under conditions of incomplete thermal contact between contacting bodies is obtained. Asymptotics of the obtained solution for small and large values of time are determined. For the materials of a cermet layer–iron base friction pair, we investigate the influence of the thermal conductivity coefficient of the contact on the temperature distribution and intensity of a heat fluxes.     

Interaction between two neighboring circular holes in a prestretched simply supported orthotropic strip under bending

In this work, the influence of initial stretching of a simply supported plate-strip containing two circular holes on the stress concentration around the holes caused by bending of the strip is examined using the finite-element method. The mathematical formulation of the corresponding boundary-value problem is presented within the frame work of the three-dimensional linearized theory of elasticity (TDLTE) under a plane strain state. The material of the plate-strip is linearly elastic, homogeneous, and orthotropic. The numerical results obtained in investigating the influence of the initial stretching and the location of holes on the stress concentration are presented. In particular, it is established that the initial stretching significantly decreases the stress concentration at some characteristic points on the contour of the holes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 827–838, November–December, 2008.     

Two-stage stochastic problems with correlated normal variables: computational experiences

Two-stage models are frequently used when making decisions under the influence of randomness. The case of normally distributed right hand side vector – with independent or correlated components – is treated here. The expected recourse function is computed by an enhanced Monte Carlo integration technique. Successive regression approximation technique is used for computing the optimal solution of the problem. Computational issues of the algorithm are discussed, improvements are proposed and numerical results are presented for random right hand side and a random matrix in the second stage problems.     

Influence of physical nonlinearity on resonance vibrations and dissipative heating of inelastic rectangular plates

On the basis of a concept of complex characteristics, we present a statement of nonlinear conjugate problems of forced resonance vibrations and dissipative heating of inelastic plates of physically nonlinear materials, for which the real and imaginary parts of mechanical complex characteristics depend on the amplitude of deformations. Numerical-analytical methods for the solution of the indicated nonlinear problems are presented. An analysis of the influence of physical nonlinearity on the amplitude–frequency and temperature–frequency characteristics and on the coefficient of damping of vibrations of rectangular plates is performed.     

Fatigue failure criteria and degradation rules for composites under multiaxial loadings

To develop design rules for dynamically loaded composite structures, extensive static and cyclic tension/compression-torsion tests were carried out on carbon-fibre-reinforced composites, in which especially the important influence of multiaxial loading conditions on their fatigue behaviour was investigated. Physically based failure criteria for static loadings are modified for multiaxial cyclic loadings, and a good agreement with experiments is achieved. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 631–641, September–October, 2006.     

Correlation between the strength of fiber-reinforced plastics and the adhesive strength of fiber—Matrix joints

The relationship between the strength (σc) of unidirectional fiber-reinforced plastics in different stressed states and the interfacial strength of their components is investigated. The shear adhesive strength (τ0) of fiber—matrix joints determined by the pull-out technique is used as a measure of the interfacial strength. To obtain the correlation curves betweenσc andτ0, the experimental results are used, where both the plastic and adhesive strength change under the influence of a single factor. In this case, such factors are the fiber surface treatment, nature and composition of polymer matrices, and test temperature. It is shown that the strength of the glass, carbon, and boron plastics increases practically linearly with increased interfacial strength. Such a behavior is observed in any loading conditions (tension, shear, bending, and compression). Sometimes, a small (10–20%) increase in the adhesive strength induces a significant (50–70%) growth in the material strength. Therefore, the interface is the “weak link” in these composites. The shape of theσc—τ0 curves for composites based on the high-strength and high-modulus aramid fibers and different thermoreactive matrices depends on the nature of the fiber and the type of stress state. In many cases, the composite strength does not depend on the interfacial strength. Then, the fiber itself is the “weak link” in these composites. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 291–304, May–June, 2000.     

Cryogenic mechanical response of multilayer satin weave CFRP composites with cracks

We deal with the thermomechanical response of multilayer satin weave carbon-fiber-reinforced polymer (CFRP) laminates with internal and/or edge cracks and temperature-dependent material properties subjected to tensile loading at cryogenic temperatures. The composite material is assumed to be under the generalized plane strain. Cracks are located in the transverse fiber bundles and extend to the interfaces between two fiber bundles. A finite-element model is employed to study the influence of residual thermal stresses on the mechanical behavior of multilayer CFRP woven laminates with cracks. Numerical calculations are carried out, and Young’s modulus and stress distributions near the crack tip are shown graphically. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 479–492, July–August, 2008.